A pair-formation model for hepatitis B virus transmission dynamics

Abstract

Hepatitis B virus (HBV) transmission among adults is strongly shaped by stable sexual partnerships, yet many models assume homogeneous mixing. We develop and analyse a sex-structured HBV model with explicit pair formation or dissolution, vaccination, treatment, and a simplified representation of vertical transmission (12 single and 36 paired compartments; 48 ODEs). Positivity and boundedness are established, and the basic reproduction number R 0 is derived using a next-generation formulation adapted to partnership dynamics. Using Kagera Region (Tanzania) initialisation, 10-year numerical simulations show that homogeneous mixing (NP) yields a total-prevalence peak of ≈ 23 – 24 % and ≈ 5 . 5 % by year 10, whereas the pair-formation model (PF) peaks at ≈ 6 % and declines to ≈ 1 . 2 % by year 10; chronic carriage is ≈ 1 . 0 % under PF versus ≈ 5 . 0 % under NP. Intervention experiments give final prevalence 5.25% (no control), 4.66% with reduced partnering ( ≈ 11 % reduction), 1.59% with increased recovery ( ≈ 70 % reduction), and 1.37% for the combined strategy ( ≈ 74 % reduction). Sex-specific scenarios yield M/F prevalence ratios 0 . 89 – 1 . 03 . Overall, partnership structure materially alters HBV projections, and treatment-centred control delivers the largest gains, strengthened by vaccination and targeted behavioural or partner-based measures. Thus, these findings demonstrate the importance of stable partnership structure for realistic HBV projections and support treatment-centred strategies in stable-union settings. • A population-based pair-formation model is developed to describe Hepatitis B virus transmission dynamics. • Explicit representation of single and partnered individuals captures key behavioural and demographic effects on HBV spread. • Partnership formation and dissolution substantially modify transmission potential and equilibrium outcomes. • Analytical results characterise reproduction thresholds and stability of disease-free and endemic equilibria. • Numerical simulations demonstrate the epidemiological impact of structured partnerships on HBV persistence and control. • The framework provides generalisable insights for modelling sexually transmitted and blood-borne infections.